Minimum Norm Method for Linear and Planar Sparse Arrays

Abstract: Coprime and nested arrays are sparse arrays with enhanced degrees of freedom, which can be exploited in direction of arrival estimation using algorithms such as product processing, min processing, and MUSIC. This paper applies the minimum norm method for direction of arrival estimation. Comparison of the root mean squared errors and probabilities of resolution of the minimum norm method with MUSIC for a given linear coprime or nested array demonstrates the superiority of the minimum norm method. Specifically, minimum norm method exhibits lower mean squared error, narrower peaks at the locations of the true sources, and a lower noise floor in the spatial spectral estimate. This work also formulates two different minimum norm methods for planar sparse arrays: direct and linear. Comparison of the linear minimum norm method with the linear MUSIC for planar arrays also demonstrates higher accuracy of the minimum norm method.